Curvature Bounds for Neighborhoods of Self-Similar Sets
Curvature Bounds for Neighborhoods of Self-Similar Sets
复制标题
自相似集邻域的曲率界
DOI：
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复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
S. Winter
中科院分区：
文献类型：
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作者：
S. Winter
In some recent work, fractal curvatures C^f_k(F) and fractal curvature measures C^f_k(F, .), k = 0, ..., d, have been determined for all self-similar sets F in R^d, for which the parallel neighborhoods satisfy a certain regularity condition and a certain rather technical curvature bound. The regularity condition is conjectured to be always satisfied, while the curvature bound has recently been shown to fail in some concrete examples. As a step towards a better understanding of its meaning, we discuss several equivalent formulations of the curvature bound condition and also a very natural technically simpler condition which turns out to be stronger. These reformulations show that the validity this condition does not depend on the choice of the open set and the constant $R$ appearing in the condition and allow to discuss some concrete examples of self-similar sets. In particular, it is shown that the class of sets satisfying the curvature bound condition is strictly larger than the class of sets satisfying the assumption of polyconvexity used in earlier results.
自相似集的分形曲率测度
DOI：
10.1515/advgeom-2012-0026
发表时间：
2013
期刊：
arXiv: Metric Geometry
影响因子：
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作者：
Winter;Zähle
通讯作者：
Zähle